"Constructive knowledge" can be assigned to Obama.

In addition to actual knowledge, the law also recognizes the concept of constructive knowlege.
Constructive Knowlege

That which exists, not in fact, but as a result of the operation of law. That which takes on a character as a consequence of the way it is treated by a rule or policy of law, as opposed to its actual character.

For example, constructive knowledge is notice of a fact that a person is presumed by law to have, regardless of whether he or she actually does, since such knowledge is obtainable by the exercise of reasonable care.

For example, possession of the key to a safe-deposit box is constructive possession of the contents of the box since the key gives its holder power and control over the contents.

Then the question becomes whether Obama took reasonable care to exercise oversight and control, as required of a president.

Which then raises the question of how much "plausible deniability" has Obama put in play re NSA, CIA, etc.

Plausible deniability is a term coined by the CIA during the Kennedy administration to describe the withholding of information from senior officials in order to protect them from repercussions in the event that illegal or unpopular activities by the CIA became public knowledge.

The term most often refers to the denial of blame in (formal or informal) chains of command, where senior figures assign responsibility to the lower ranks, and records of instructions given do not exist or are inaccessible, meaning independent confirmation of responsibility for the action is nearly impossible. In the case that illegal or otherwise disreputable and unpopular activities become public, high-ranking officials may deny any awareness of such act or any connection to the agents used to carry out such acts. The lack of evidence to the contrary ostensibly makes the denial plausible, that is, credible. The term typically implies forethought, such as intentionally setting up the conditions to plausibly avoid responsibility for one's (future) actions or knowledge.

In politics and espionage, deniability refers to the ability of a "powerful player" or intelligence agency to avoid "blowback" by secretly arranging for an action to be taken on their behalf by a third party ostensibly unconnected with the major player. In political campaigns, plausible deniability enables candidates to stay "clean" and denounce third-party advertisements that use unethical approaches or potentially libellous innuendo.

Plausible deniability is also a legal concept. It refers to lack of evidence proving an allegation. Standards of proof vary in civil and criminal cases. In civil cases, the standard of proof is "preponderance of the evidence" whereas in a criminal matter, the standard is "beyond a reasonable doubt." If an opponent lacks incontrovertible proof (evidence) of their allegation, one can "plausibly deny" the allegation even though it may be true.